Unit 3 - Multiplying and Dividing Fractions
Unit Overview
In this unit we will be focusing on multiplying and dividing fractions. Our learning will look quite different from the way these two concepts have traditionally been taught (multiply top and multiply bottom and for division invert and multiply). This approach to instruction will only develop procedural fluency, not conceptual understanding. Prior to teaching the algorithm, multiplication of fractions can be shown by the area model for multiplication. The example shows 1/3 x 1/3 = 1/9. Multiplication of a fraction by a whole number, such as 1/4 x 8 can be interpreted as one-fourth of 8 pies. If 8 pies are divided into 4 equal groups, each group has 2 pies. The multiplication of a whole number by a fraction, such as 8 x 1/4 can be interpreted as repeated addition, 8 groups of one-fourth. Examples:
Division of a whole number by a fraction, such as 8 divided by 1/4 can be interpreted as 8 represents 1/4 of _____ number. Division of a fraction by a whole number, such as 1/4 divided by 8 can be interpreted as dividing 1/4 of something into 8 pieces resulting in 1/32 size pieces. Examples:
In this unit we will address 5th grade standards: 5.NF.4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5 - Interpret multiplication as scaling (resizing) by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number 5.NF.6 - Solve real world problems involving multiplication of fractions and mixed numbers. 5.NF.7 - Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. Additional / Independent Practice (click on image for additional practice)
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I Can Statements
5.NF.4 - I CAN multiply a fraction by a fraction or a fraction by a whole number 5.NF.5 - I CAN compare the size of a product to one of the factors based on the size of the other factor 5.NF.5 - I CAN explain that when you multiply a given number by a fraction greater than one your product is greater than the given number. 5.NF.6 - I CAN solve real world problems involving the multiplication of fractions and mixed numbers. 5.NF.7 - I CAN divide whole numbers by unit fractions and unit fractions by whole numbers Vocabulary (link to online mathematics dictionary)
Learnzillion Lesson Sets (click image to access video lessons)
Standards-Based Assessment Rubric (Click to view rubric)
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